Question

Find the Integral of {e^x(1 + xInx)}/x, for x>1

Answer 1

it doesn't have a simple form.
integral ( {e^x(1 + xInx)}/x dx)
= integral ( {e^x}/x dx ) +integral( {lnx} dx )
= integral ({e^x}/x dx) + (x-1)* lnx

unfortunately integral ({e^x}/x dx) cannot be broken down into elementary functions, and is called the exponential integral, as a function: Ei(x)

so if you permit the exponential integral as an elementary function then:

Integral ( {e^x(1 + xInx)}/x dx) = Ei(x) + (x-1)* lnx +c